Generating schedules for employees is a complex problem for enterprises. Telephone call center scheduling is an example of a scheduling problem with a large number of variables. Variables include call volume at a particular time of day, available staff, skills of various staff members, call type (e.g., new order call and customer service call), and number of call queues, where a queue may be assigned a particular call type. A basic goal of call center scheduling is to minimize the cost of operators, or agents, available to answer calls while maximizing service. Quality of service, or service level, can be quantified in various ways. One common metric for call service level is the percentage of incoming calls answered in a predetermined time, e.g. thirty seconds. The call center may receive calls of various types that are assigned to respective call queues.
Traditionally, call center scheduling is performed by first forecasting incoming call volumes and estimating average talk times for each time period t (based on past history and other measures). The forecast is based upon historical data. Next, a closed-form formula known as reverse Erlang-C is used to compute full-time equivalent (FTE) agent requirements to provide a desired service level for each time period t. Such a method is described in Elementary Queuing Theory and Telephone Traffic, by Petr Beckmann, 1977 (Lee's abc of the Telephone Training Manuals, Geneva, Ill.) After the FTE agent requirements are computed, the required number of agents are scheduled for each time period t.
At a call center, calls of different types are typically placed onto different queues by an Automatic Call Distributor (ACD). The calls wait at the ACD for an operator to answer them. At many modern call centers, the agents cannot answer any type of call; they can only answer calls for which they have the prerequisite skill. At some call centers, there is a group of agents for each type of call that comes in, which means that each group (and queue of calls) can be treated as a separate problem. However, at an increasing number of call centers, agents are multi-skilled, and can answer calls from a variety of queues. Typically, not all agents have the same skills, and thus some agents can answer some calls while other agents cannot. The ACD distributes calls waiting in different queues to agents who are skilled to handle calls from the respective queues. This distribution task is referred to as skill-based routing. Determining agent schedules for this latter type of call center is known as the skill-based scheduling problem. It is considerably more difficult than the basic call center scheduling problem because of all the interactions between queues.
The skills-based scheduling problem has no known closed-form solution that can be used to estimate available FTE levels for each queue when agents are shared among queues. Prior attempts to solve the skills-based scheduling problem involve the use of a discrete event ACD simulator to validate estimates. For example, the skills-based scheduling technique disclosed in U.S. Pat. No. 6,044,355 includes forming skill groups that contain agents with identical sets of skills, preferences, and priorities. A “skill group availability array” is then generated that attempts to estimate what percentage of scheduled agents of each skill type will be available to each call type during each time interval. Erlang processing and ACD simulation are used to increase the accuracy of the percentage estimates, and standard call center schedule algorithms can then be used for scheduling.
Such prior solutions have other serious limitations. For example, the array grows exponentially as the number of skills grow. This is particularly true because the skill group is inflexible in that each different combination of skill, preference, priority, and proficiency requires the creation of a new skill group. The size of the array may thus reach a level at which processing time is too great and processing resources are inadequate. Another limitation of prior methods is that they do not allow for the easy determination of fine-grain changes to the schedule such as the addition or subtraction of a single agent. The current methods require that the entire algorithm be executed again for any incremental change, such as the addition or subtraction of one agent.
Other prior methods for skills-based scheduling use skill groups (similar to those disclosed in U.S. Pat. No. 6,044,355) and are limited to the assumption that each individual agent simply splits time at a predetermined ratio between various queues (task switching). In such methods, at any given time, each agent is limited to taking calls from queues assigned to his or her skill group at that time. Each agent is unable to take calls from other queues that he or she may be skilled in. This is a serious limitation, potentially causing some queues to overflow because the assigned skill group is busy, while there may be idle agents in other skill group who are capable of taking those calls.
Another serious limitation of prior methods is that they provide relatively coarse approximations of schedules that fail to take into account all of the dynamics of a situation. For example, if an agent from a new skill group is added to the schedule, the performance of call queues that are not handled by the new agent may change. These complex dynamics are not modeled well in available scheduling methods.
Another limitation of current methods is that simulation must be performed for each iteration of the algorithm. One reason for this requirement is the failure of prior methods to estimate individual contributions of single agents to particular queues. This is expensive and time consuming.
Yet another disadvantage of prior methods for solving scheduling problems is that the algorithms of prior methods may require excessive time to execute because the prior methods are not designed to facilitate parallel processing.